Theory and Experiments on Spatial Competition

Article excerpt

I. INTRODUCTION

Why do convenience stores tend to choose dispersed locations close to consumers, whereas fast food restaurants tend to locate near each other? Why do automobile dealers locate close to one another, yet go to great effort to differentiate their products through advertising? It is clear that firms can compete on many dimensions including price, location and product characteristics. Previous work that has sought to explain competition on many dimensions has been less than successful (see Osborne and Pitchik |1987~).

In our investigation, we allow competition to occur only in the form of spatial product differentiation. In the spirit of Hotelling |1929~, each firm selects a location at some point on a line segment. Identical consumers with downward sloping demand curves are uniformly distributed over the market. Customers incur a transportation cost which varies linearly with their distance from the closer firm. The FOB (free on board) price charged by each firm is the same and exogenous. The price paid by a consumer is the sum of the fixed FOB price and the transportation cost. This gives a negative relationship between a customer's distance from the nearest supplier and the quantity demanded.

A firm has two considerations when selecting a location: market share and proximity to consumers. When the firms locate symmetrically, each at a distance of one-half from the center of the market, they split the market in half. Each firm obtains a 50 percent market share and the most remote consumer is a distance of only one-fourth of the total market space away from one of the firms. Because of this, by locating at the quartiles of the market the firms maximize combined sales. However, in this situation a firm can typically increase it sales by moving toward its rival, thereby increasing its market share as buyers switch firms.

The decision to locate away from the center of the market carries a degree of risk. Any position away from the center leaves "unprotected" market share. The other firm has an opportunity to gain market share (and profit) by locating close by, but a little closer to the center. By locating at the center of the market, a firm assures itself of at least one-half of the market regardless of the other firm's location. Thus market share is secure. In this case, the firms share the market equally, the most remote customer is a distance of one-half from each firm, and combined sales are relatively low compared to a quartile outcome. This corresponds to the notion of minimum differentiation that is attributable to Hotelling. However, if the transportation cost is sufficiently high, this is unlikely to be the outcome.

The theory of location choice has been considered by economists and political scientists. Smithies |1941~, Eaton |1972~ and Eaton and Lipsey |1975~ all consider a uniform distribution of consumers over a linear market. Using verbal arguments Smithies shows that for a duopoly facing linear demand, the type of equilibrium depends on the ratio of the transportation cost to the choke price(1) on the demand curve. Eaton provides the mathematical details. Eaton and Lipsey consider unit demand and extend the analysis to n-firms and a two-dimensional market. In a duopoly on a linear market they conclude that the firms will locate at the center.

Hinich and Ordeshook |1970~ consider a competition for votes between political candidates.(2) They show the candidates will choose the same location in equilibrium if each candidate's objective is to maximize plurality (the excess of its votes over its opponent). However, if each attempts to maximize votes, the candidates may choose different positions in equilibrium, depending on the sensitivity of voter preferences. Much of their analysis is analogous to the case of unit demand and linear transportation cost.

Gabszewicz and Thisse |1986~ maintain unit demand and conclude that due to the harsh competition that such an environment fosters, "the only location equilibrium consists of both firms clustered at the center of the market. …